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Spontaneous Symmetry Breaking in Quantum Field Theory
By Evan Hughes
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This paper describes a brief history of symmetry and symmetry breaking in physics, describes the concepts of symmetry and symmetry breaking (both spontaneous and explicit, and explores spontaneous symmetry breaking in quantum field theory, giving examples accompanied by Feynman Diagrams and simplified Lagrangian equations. Finally, some examples of spontaneous symmetry breaking are given for classical systems.
LanguageEnglish
PublisherEvan Hughes
Release dateJan 1, 2015
ISBN9781311582812
Author
Evan Hughes
Born in Texas but raised in Germany, Evan Hughes grew up in the land of fairy tales. His previous works include articles in the "Stuttgarter Algemeine" and several poetry anthologies, including "Patchwork" and "Musings". Most recently, one of his fairy tales can be found in the anthology "Merry Sorrows (Un)Happy Endings." Poetry infuses his fiction, giving it a unique musical rhythm.Evan holds a Bachelor of Arts degree in Physics from Pitzer College, and is the author of a series of articles on physics for laypeople. He has observed an extra-solar planet using Pomona College's 1m telescope at Table Mountain Observatory, and made use of the Very Large Array in New Mexico to study the Fornax A radiogalaxy.
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Spontaneous Symmetry Breaking in Quantum Field Theory - Evan Hughes
Spontaneous Symmetry Breaking in Quantum Field Theory
Evan Hughes
Spontaneous Symmetry Breaking in Quantum Field Theory
Evan Hughes
Published by Evan Hughes
Copyright © 2009 by Evan Hughes
Atlanta, GA 30316
° ° °
Originally published in partial fulfillment of Charles Evans Hughes II’s Senior Thesis in Physics to the Joint Science Department of the Claremont Colleges, April 11, 2009.
Charles Evans Hughes II and Evan Hughes are the same individual.
° ° °
Thank you for downloading this ebook. This book may be reproduced, copied, and distributed for educational purposes only provided any content so used remains in its original form only and proper attribution is given.
CONTENTS
Abstract
Introduction
Historical Background
Symmetry
Symmetry Breaking
Methods and Discussion
The Lagrangian
Case 1
Case 2
Case 2a
Case 3
Case 3a
Quantum Decoherence
Three Examples of Spontaneous Symmetry Breaking in Classical Mechanics
Conclusions
Future Directions
References
ABSTRACT
Spontaneous symmetry breaking (SSB) plays a crucial role in physics. Its effects can be seen in both classical and quantum mechanics. Without SSB, our universe would not exist as we know it. As such, it is essential to expand our understanding of this phenomenon. To this end, we begin by discussing the history of symmetry and asymmetry in physics. After defining SSB, we explore the roles of spontaneous symmetry breaking and demonstrate certain instances of SSB. We then use the Langrangian formulation, an essential tool for understanding Quantum Field Theory, to determine the potential energy states for some two particle systems. We also address the role of SSB in the quantum decoherence of bodies. Through these methods, we achieve a better understanding of the physical
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